From 6eb85d220c92f53a481d0e0584a28e6c07acab2b Mon Sep 17 00:00:00 2001 From: didericis Date: Mon, 25 May 2026 02:58:16 -0400 Subject: [PATCH] face_monochromatic_pairs: fix Remark 5.6 formatting The disproof of Conjecture 5.5 used \[ ... \qquad\text{and}\qquad ... \] to give both cycle definitions on a single display line. The second half was too long to fit, producing a wide gap and an ugly line break. Switch to align* with the two definitions stacked and aligned at =. Co-Authored-By: Claude Opus 4.7 --- papers/face_monochromatic_pairs/paper.pdf | Bin 1220292 -> 1220261 bytes papers/face_monochromatic_pairs/paper.tex | 9 ++++----- 2 files changed, 4 insertions(+), 5 deletions(-) diff --git a/papers/face_monochromatic_pairs/paper.pdf b/papers/face_monochromatic_pairs/paper.pdf index 37bb4de792da0a21d93cd2e4d97bb3f50f6c7d30..7069c7c6de271650cdc09f2970e7a15c41a9e479 100644 GIT binary patch delta 22841 zcmV(-K-|B?y-KCMN`Qm`gaU*Egam{Iga(8Mgb0KQgbK6^1knOBHIv{QDSypdNq5}F z5x(nJ@c9z(S!neRzfNI!FGO}^S(d2u=-t_ounDsoTGEWA88oereu`ck3#p=K$4W#e&*Sf2 zfB*XAAhc=zm^H*e|o+4q0N3lY70`J7r_xVQfChMG@a zzw*}{yS#q${JY~=Cn|}AI{w$Yzdd;&`BBC)D=n@q)*RNE9K}+xOwiKaZ3=iLO`?mU zIWN|9U98VtYZ{#%#}e+VdVAi|v#y>#sk;p|udY_dv52Z;5fymRK7WQ~NfWg-Jukcd z{bP9T@>r&ke^PAMI~WV@%Pltd9e=04%T2k$<_%3-m43bT*6&bFcF2!nAy{TCZSJ1| zBBYGN1*Z-_bHf9}D3&I=@AIwiASb7sGHoTy#dM~r*J)rX%{UiFlTI+5@crzhpJhDF zh9wE514~L-YE0kfqkry8%=Wbk@5^M@_7y9o@X(af(OKQB3To*#{l)a)v0+tj+b$o@ z9N+7PN9A@^t_w!9gFKD1%QRsk9e2t-tLrIAV`YHXIr6$>#xL`vZtAMan=6xpdkIP8-(~PrCWZq?xb=O{SOy;2M|7$}%-u{%mCyxN#uVUxK5g*+76(M@i(LEXrH@2aN*%si*SA zMNZ9zDNs*JtA8lpuBoXCpMlg&T@x8I@4`mG^lN}#z=0Y%WtrDVo@hl0^3c%S^%?$a zFCoy-UDnj{Eo#w=UB4k{alF?K?*&$>@qlh7R;C7a>NX9IUhmI0e(sH*3GBeJkr5aG zc)q4Kx;_VSjI}Y*H^Bu+!BS9)eu7PaI}8I-I^|++T7RbS%Efmo{kFGt=V{?q?sP{- zq?VaxMlMJlG!Q}q<0ZH0QF8}9YLjgMb(GUz*Oa@e z2&pN{Op^Q&egDE4*{5Kft&RMUbLax+V`k?g0%K|?l#@4Fn=iqu=8%?RD|TDDx`>Zpg)_!0n)N9 zsw;X*Dh@7IdF!w8ZC+iq{cFHLYu~k||6Nm~@&C;s0P6J0n-O>lX5G$ukXw0H|2)yRsi2C=u=QvcW6vm=#;-Y15S}G}qi#}50#)=N zLVuSff_EHmUH;64DjFwEIOWSC$4Ps%HvF!szuVaU0s)wQNZ3Qt?Vt)f^H37}tBQ)9Vp$vr7nU4Oq+vhaLiZ@gs(`1&mx@7VK<^42?qWqXu* zXD|y#+-pgv!%%-A!41M$6FBljvqb5soj94mZg^8lI_+e6+KD@DRGM4r*3DP~9-x~T zx0~Ga4Ro1q9PfMBg4e$Xb|wL}C@Du1CE(p>uiicn2|b8gDy}P<*?=>x8v@^;^M3?W zLe3q<8&Eh{9X<%v%Mbum&S_epP>m>*l*4L&3NEZ`*;VW0oX|g;>JCSiwQtg_1+y^0C#6h%bTDiV2=?*A#^br9Ei~G=ldR} z3C$sy9_g9~yyDFHmwbX7P!J@8d4J}DcNWAHlbwfQOg1vp(=aNL>1_HB8bJkiI2+;o zw(~=e1;96XEO0S;EHeQ>pJ;gJ?7+H*4yWF-uL45>VzgYV0Q7@d|1vZLIK!i% zK6Fsxwu6#?u7d(KY@;px1zjP)G9z6=ylt4Y_O_E3qaJe-c34S)mzreB!hiD5kofh$ z4i6)2ZjNSAE$@Ol#tUpjf{!k5Ww&7`xo5Z2FuRR=xRoaHw-W~$R@Vn-;4)8dq9^g_-N0L-d{p2*a=#+@ndKAc=u4lPJfn5}n^9(b^sGy=V;3 zx2Lfb2WTu^!1Kl!L^6i%+JF6OL!&wH7uc6%!@i#f)lVkVd${U%lZ*pC>dm2C5bV)M zJs8U6);z?%^lkeJa^Su8Wtklzfej4A?`{U31~rcuSs1tMz{4MF%BKY|LVC9#pT0>Cm^7Vk-nrngy;*F}?K9}>T5xv8Y{x^ULvA_A zKd2kb!RZjqWtswh0fP?USEvUebG9IJFe)%X4;W?*xlLLFW-*HZ#{9HQ8a^$9mfd{H z(=vC_c;@b><%3nJWPdiD$Ew~?W+88W4Y{nKSw?eUm_>7!xDEcbY^Q+^#kv0%Gshm= zf!7bLQNRSL5et9!8blvD1V*MQd%l>fMT`fJz$35PP#_wJq0AJiDiysb&;1-CvNTok zep8-e5|{$^38+5+H8XBPw^0}j9Icw7LpK@l^{U=esG?|!_ka1tt}4DbjxEoI-rl)} z%ig($x6T`MtOIfd?z|ll(96(%6q9lQ?-={Qu{EcG=dn0^;vIK*=2ryA>SG{{->ecW zRSTz8#V&fXy1@-kG!vOwz^O%=AyqS=K*O~Zg=&iRlhbNnJUMTQV%z6vwNHwvX=WX7 zPl*}35Z&NZnSW9!{UBt0Q21^#2&)LFFCYaU(`HWtBLViagHpn6gw6`s->RuFe~E#s zbWA$e`>qelrSY;x;W0fpVD4ed2v%bOQUciL4`7TNwrp?P^5_-fp#}DgX*M-;(w2J` za!6Gx%7sj*aMt7(zTfB6VGrck^&A^l#aZWH1oT?vYkzpUE}GA%tu5C@uZut(a;CL$ z`jGeaB#2^A2#t@oYn?^Jm2u91kWFEi=m8*=bLFiU)>t@e!QGXNW@R z!7?F}`&ic{s@3z8_?b&wMItbg8-fawgGlQ!+~HR2bj(06xagHk@t!)g;Pkr(E`0?J zMZUs-?SF>#3Pv$)7U|EgtNJvrs?h#5XQ@cnp{g{X6H##8 z?dO92aknZnk+6NYsYb?GL1)>WF)HQkMvO>`6w0~|Yy_mX&trJSPL{aO?YUm4M=VdNM zHGW>!+sCvTET>W~%|iacRBgN4Nd!KSqZrBvl#DLQ)?dMrE=VO5WNXU?lV+)Q_FQW! 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